Black vultures excel at gliding flight; they can move long distances through the air without flapping their wings while undergoing only a modest drop in height. a vulture in a typical glide in still air moves along a path tipped 3.5∘ below the horizontal. if the vulture moves a horizontal distance of 100 m, how much height does it lose?

The vulture loses 6.1 m height

Explanation:

Please see the attached figure.

The horizontal distance and the loss of height form a 90º triangle.

The loss of height is  the side opposite the given angle (3.5º) and the 100 m horizontal distance is adjacent the angle.

Then, using trigonometric rules:

(1)   sin 3.5º = h / hyp

(2)  cos 3.5º = distance / hyp

where

h = height lost during the flight.

hyp = hypotenuse of the triangle

Using (2) we can calculate the hypotenuse:

cos 3.5º = 100 m / hyp

hyp = 100 m / cos 3.5º = 100.2 m

with the hypotenuse we can now calculate the loss of height using (1):

sin 3.5º = h / hyp

sin 3.5º = h / 100.2 m

sin 3.5º * 100.2 m = h

h = 6.1 m

( very modest drop in height indeed!)